pat1066. Root of AVL Tree (25)

1066. Root of AVL Tree (25)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

         

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print ythe root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

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提交代码

#include<cstdio>
#include<cstring>
#include<iostream>
#include<stack>
#include<set>
#include<map>
#include<queue>
#include<algorithm>
using namespace std;
struct AVLtreenode{
    int h,v;
    AVLtreenode *l,*r;
};
#define max(a,b) (a>b?a:b)
int GetHeight(AVLtreenode *root){
    if(!root){
        return 0;
    }
    return root->h;
}
AVLtreenode* AVLRightRotation(AVLtreenode* root){
    AVLtreenode* temp=root->r;
    root->r=temp->l;
    temp->l=root;
    root->h=max(GetHeight(root->l),GetHeight(root->r))+1;
    temp->h=max(GetHeight(temp->r),GetHeight(root))+1;
    return temp;
}
AVLtreenode* AVLLeftRotation(AVLtreenode* root){
    AVLtreenode* temp=root->l;
    root->l=temp->r;
    temp->r=root;
    root->h=max(GetHeight(root->l),GetHeight(root->r))+1;
    temp->h=max(GetHeight(temp->l),GetHeight(root))+1;
    return temp;
}
AVLtreenode* AVLRightLeftRotation(AVLtreenode* root){
    root->r=AVLLeftRotation(root->r);
    root=AVLRightRotation(root);
    return root;
}
AVLtreenode* AVLLeftRightRotation(AVLtreenode* root){
    root->l=AVLRightRotation(root->l);
    root=AVLLeftRotation(root);
    return root;
}
AVLtreenode* AVLInsert(int num,AVLtreenode *root){
    if(!root){

        //cout<<1<<endl;

        root=new AVLtreenode();
        root->h=1;
        root->l=root->r=NULL;
        root->v=num;
        return root;
    }
    //cout<<2<<endl;
    if(root->v>num){//插入左子树
        root->l=AVLInsert(num,root->l);
        if(GetHeight(root->l)-GetHeight(root->r)==2){//需要左旋
            if(root->l->v>num){//单左旋
                root=AVLLeftRotation(root);
            }
            else{//左右旋
                root=AVLLeftRightRotation(root);
            }
        }
    }
    else{
        root->r=AVLInsert(num,root->r);
        if(GetHeight(root->r)-GetHeight(root->l)==2){//
            if(root->r->v<num){//
                root=AVLRightRotation(root);
            }
            else{//
                root=AVLRightLeftRotation(root);
            }
        }
    }
    root->h=max(GetHeight(root->l),GetHeight(root->r))+1;
    return root;
}
int main(){
    //freopen("D:\INPUT.txt","r",stdin);
    int n;
    scanf("%d",&n);
    int i,num;
    AVLtreenode *root=NULL;
    for(i=0;i<n;i++){
        scanf("%d",&num);

        //cout<<"i: "<<i<<endl;

        root=AVLInsert(num,root);
    }
    cout<<root->v<<endl;
    return 0;
}